Resistors such as are described in FIGS. 1A, 1B, and 1C are frequently formed in integrated circuits (IC). They typically are comprised of a resistor body 100, 102, and 104 with a resistor head 110 at each end to which electrical contact is made. The IC resistors may be formed using a well in the substrate, may be formed by gate material such as polysilicon or metal, may be formed using implanted n-type or p-type diffusions, or may be formed using a variety of metals in the interconnection layers.
The resistors 100, 102, and 104, shown in FIG. 1A, 1B, 1C, may be formed with the same resistor length 122 or with different resistor lengths, LR. The hundreds or thousands of resistors that are formed in an integrated circuit typically have a variety of different resistor widths, 114, 116, 118.
It is desirable for the total resistance RT (body resistance plus head resistance) to vary linearly with the length LR and linearly with 1/WR which is the inverse of the resistor width WR. Ideally when the resistor body length LRB is zero, the total resistance RT would be equal to the resistor head resistance RH. Since the resistor heads 110 are identical for the three resistors 100, 102, 104 in FIGS. 1A, 1B, and 1C when the length of the three resistor bodies LRB is extrapolated to zero the head resistances RH should be the same. As shown in FIG. 2 this is not the case for the resistors depicted in FIGS. 1A, 1B, and 1C.
This discrepancy may cause circuit simulation programs which assume ideal behavior to calculate an incorrect result. This may cause the circuit to fail or may result in a reduction in the design space with a corresponding reduction in IC yield.